The power of beauty

A science experiment can be as beautiful as a landscape, person or painting - and have a similarly profound effect, says Robert Crease

Can a science experiment be beautiful? And could school students appreciate the beauty of a science experiment?

Things are ordinarily called beautiful if they reveal something about ourselves or nature with clarity, simplicity and depth. A thing is beautiful if it pulls us out of our confusion to show us something directly, and allows us to grasp it without needing to make further inferences or ask more questions.

Recently, I polled readers of the international physics magazine Physics World, whose circulation includes a large number of professors and secondary school teachers, for their thoughts on beautiful experiments in physics. The overwhelming response convinced me that experiments can be beautiful in the same way that a landscape, person or painting can be beautiful.

As teachers know, background knowledge can intensify a student's ability to appreciate beauty - in science, as well as in nature and art. Careful coaching can allow young students to appreciate the beauty of an experiment - and beauty is your ally as an instructor.

Beautiful scientific experiments have several things in common. Structurally, they are relatively simple and economical: they do not require a lot of complicated hardware to construct or calculations to understand. They are also playful: they can be executed by students and repeated in myriad variations. Finally, they make some important feature of nature perceptible to the senses immediately, cleanly and with finality. There are no remaining questions.

Students can immediately appreciate that such an experiment is not something abstract. It's a little performance that you instruct students to stage themselves to find out something. They put together the props and follow the scripts - and, as with any performance, it takes tinkering to get it right.

For a while it may frustrate, but once the students have mastered the physical manipulations an underlying pattern suddenly emerges from things that seemed chaotic, random and arbitrary. That's what makes an experiment beautiful.

Student scientists can gain an aesthetic and intellectual pleasure that is not significantly different from the experience of beauty in the arts. They want to stay and linger over it, and experience it again and again.

Textbooks try to keep the beauty of experiments secret, of course. Experiments are treated as a means merely to get the student to acquire knowledge. Students themselves may take this at face value and overlook the beauty of experiments they are assigned, viewing them merely as tasks to be accomplished on the way to passing a course.

But beautiful experiments are in a different class from other exercises: they can have a deep, lasting and highly personal impact. One respondent to my poll remembered such an experience decades ago in a college physics lab when he performed the Millikan oil-drop experiment (in which the electrical charge on an electron is determined by measuring the rate at which tiny oil droplets rise and fall in an electric field). He recalled: "I literally sat in my college room, staring at the spreadsheet, dumbfounded at how perfect and elegant the whole thing was. I redid the analysis just for the fun of seeing it come out again." (Robert Millikan won the Nobel Prize in Physics for this work.) Another respondent described her reaction to the electron two-slit experiment (which proves that electrons behave like waves). It was "like watching a total solar eclipse for the first time: a primitive thrill passes through you and the hairs on your arms stand up".

Cultivating the students' appreciation of beauty creates an atmosphere in which the learning of science flourishes. It is difficult to imagine a person wanting to become a scientist today, with all the career risk involved, without such an appreciation.

Many classic beautiful experiments can be carried out, with different levels of complexity, in secondary and even primary schools. Some can be performed with simple equipment, such as blocks, balls, timers and prisms. And an astonishing array of more advanced experiments can be carried out thanks to equipment developed by organisations like the Wright Center for Science Education at Tufts University.

One such experiment follows Galileo's procedure of rolling balls down inclined planes to discover the rule which bodies obey when they fall. It can be performed by students of many levels, to varying precision.

Galileo first conducted this experiment successfully in 1604. But for years before that he did not know if there was an experiment that could allow him to discover any law concerning falling bodies. His first attempts failed because he found that falling bodies were too difficult to measure. Seeking to slow down the fall, he experimented with pendulums, but found these taught him little on the subject.

Around 1600, he began to build inclined planes with grooved tracks down the middle and tried to measure how quickly balls rolled certain distances down them. But he was unable to get satisfactory results and his work was further delayed by illness.

The breakthrough came when he was able to demonstrate the law for which he was looking: the distance traversed by an object depends on the square of the time it is accelerated. If the time increases in even units (1, 2, 3...), this means that the distance traversed by the object between each succeeding beat increases according to the odd-numbered progression (1, 3, 5...).

The way Galileo describes his experiment in his Discourses Concerning Two New Sciences is clear enough for students: "A piece of wooden moulding or scantling, about 12 cubits long, half a cubit wide, and three finger-breadths thick, was taken; on its edge was a cut a channel a little more than one finger in breadth; having made this groove very straight, smooth and polished, and having lined it with parchment, also as smooth and polished as possible, we rolled along it a hard, smooth, and very round bronze ball. Having placed this board in a sloping position, by lifting one end some one or two cubits above the other, we rolled the ball, as I was just saying, along the channel, noting, in a matter presently to be described, the time required to make the descent.... (in) such experiments, repeated a full hundred times, we always found that the spaces traversed were to each other as the squares of the times, and this was true for all inclinations of the plane, i.e., of the channel, along which we rolled the ball."

The "presently to be des-cribed" device to measure time was a water-clock, in which the amount of water that flowed through a small pipe during the time of descent was collected and measured.

Science historian Thomas Settle reconstructed this experiment, water-clock and all, as a student and wrote it up in Science magazine, complete with diagrams and data tables. His four-decades-old article is an excellent guide to reenacting the experiment. His basic equipment consisted of a long pine plank; a billiard ball; a set of wooden blocks; and, for the water-clock, a flowerpot threaded by a small glass pipe and a graduated cylinder.

The most difficult part of the reconstruction is using a water-clock, which is notoriously unreliable over short periods. For a long time, science historians could not believe that Galileo had been able to achieve enough accuracy with one to establish the law of accelerated bodies. They assumed he had first discovered the law, then built the device to demonstrate it.

Galileo's biographer Stillman Drake has challenged this. By studying a page of Galileo's notebook, he proposes that Galileo did arrive at the law using the inclined plane method, but not by measuring time with a water-clock. Instead, he suggests that Galileo, a competent lute player, used his skills as a musician to mark out a rhythm with much more accuracy than any water-clock could measure.

Drake proposes that Galileo put frets made from gut strings on the track, similar to those used as frets on early stringed instruments. When a ball rolled down the track and passed over a fret, he would hear a faint noise. He then adjusted the frets so that a ball, released at the top, struck the frets in a regular tempo - which for the typical song of the day was just over half a second per beat.

Once Galileo had set the tempo, all he had to do was measure the distances between the frets. These grew longer as the ball picked up speed, illustrating the 1, 3, 5... progression and allowing him to compose the more elaborate experiment reconstructed by Settle.

As Drake's work shows, this experiment can be carried out in many ways. It can be adapted to many student levels, as confirmed by descriptions that schools ranging from elementary to graduate level have posted on the internet. Besides Settle's Science article, other good sources are the Galileo web pages of Rice University and the website of Professional Development, whose inclined plane experiment uses "Hot Wheels" tracks (see below).

In carrying out the experiment yourself, it is useful to keep the inclined plane shallow - about 10 degrees from horizontal. Use a grooved track so the ball does not fall off and ensure that the ball and track are as frictionless as possible. The experiment is relatively simple and economical, is fun to set up and do, makes the result stand out clearly and convincingly, and reveals something new about nature. Beautiful!

Ultimately, the beauty of this experiment lies not in the mathematical law of accelerated motion that we find thanks to it, but rather in the dramatic and convincing way in which a relatively simple apparatus can allow a fundamental principle of nature to appear in what looks at first to be a set of random happenings.

Robert P Crease is a Senior Fellow at the Dibner Institute for the History of Science and Technology at MIT

ACCELERATED LEARNING WITH THE GREAT GALILEO

Galileo's experiment to measure the acceleration of free fall, "g", can be recreated using a track and a motion sensor.

The theory is that if a is the cart's acceleration down the track, and q is the angle that the ramp makes with the horizontal, then from the diagram:

g = gsinq = g hl = (gl)h

The graph of a vs.h should be a straight line, with slope gl.

Measuring h and l is straightforward. The acceleration, a, can be determined from the slope of the velocity vs. time graph produced by the motion sensor.